Multiples mitigation and imaging with incomplete seismic data

A system comprising at least one non-transitory storage medium storing instructions that upon execution cause the system to:

• receive observed survey data acquired using survey receivers;
• while a stopping criterion is not satisfied, iteratively performing:
• generating synthetic survey data using a wave propagator based on a current model of a target structure;
• and
• modifying the current model to reduce a difference between the synthetic survey data and the observed survey data, while maintaining unchanged a velocity component of the current model, wherein the modifying of the current model produces a modified model;
• and
• in response to the stopping criterion being satisfied, use the modified model produced by a latest iteration of the modifying to reduce an effect of multiples in the target structure.

A computer comprising:

• a storage medium to store observed survey data;
• and
• at least one processor configured to:
• generate synthetic survey data using a two-way wave propagator based on a current model of a target structure;
• modify the current model to reduce a difference between the synthetic survey data and the observed survey data;
• while maintaining unchanged a velocity component of the current model, wherein the modifying of the current model produces a modified model;
• and
• use the modified model to reduce an effect of multiples in the target structure.

A method of processing seismic data from a seismic survey of a subterranean section of the Earth, comprising:

• receiving, by a system including a processor, survey data recorded by a seismic receiver containing primaries and free-surface multiples, wherein the recorded survey data as a result of incomplete sampling in the seismic survey comprises incomplete seismic data;
• receiving;
• by the same system, the shot and receiver geometry of the seismic survey producing the recorded survey data;
• splitting, by the system, the recorded survey data into up-going and down-going wavefield components on a recording surface;
• generating, by the system, synthetic survey data on the recording surface using a source wavelet and a wave propagator based on a current model of a target structure, wherein recorded down-going wavefield components are used to replace corresponding components in a synthetic down-going wavefield during propagation and the synthetic survey data is used to provide substitute data for at least some incomplete parts of the recorded survey data such that complete synthetic survey data is generated from the recorded survey data and the synthetic survey data;
• modifying, by the system, the current model of the target structure to reduce a difference between the synthetic survey data and the recorded survey data while maintaining unchanged a velocity component of the current model, wherein the modifying of the current model produces a modified model;
• and
• using the modified model as an image of the target structure that is illuminated by both primaries and free-surface multiples.